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Spontaneous polarization induced doping in quasi-free standing epitaxial graphene on silicon carbide from density functional theory

By means of density functional theory (DFT) calculations we have quantitatively estimated the impact of the spontaneous polarization (SP) of the SiC(0001) substrate on the electronic properties of quasi-freestanding graphene (QFG) decoupled from the SiC by H intercalation. To correctly include within standard DFT slab calculations the influence of the SP, which is a bulk property, on a surface confined property such as the graphene's doping, we attach a double gold layer at the C-terminated bottom of the slab which introduces a metal induced gap state that pins the chemical potential within the gap. Furthermore, expanding the interlayer distances at the bottom of the slab creates a local dipole moment which counters that arising from the slab's polar character and allows to align the location of the graphene's Dirac point (DP) for cubic SiC(111) with the chemical potential. Thus, the DP shifts obtained for other polytypes under the same slab model become an almost direct measurement of the SP-induced doping. Our results confirm the recent proposal that the SP induces the experimentally observed p-type doping in the graphene layer which can achieve DP shifts of up to several hundreds of meV (or equivalently, $\sim 10^{13} e$/cm$^2$) for specific polytypes. The doping is found to increase with the hexagonality of the polytype and its thickness. For the slab thickensses considered (6-12 SiC bilayers) an ample, almost continuous, range of doping values can be achieved by tuning the number of stacking defects and their location with respect to the surface. The slab model is next generalized by performing large scale DFT calculations where self-doping is included in the QFG via point defects (vacancy plus a H atom) thus allowing to estimate the interplay between both sources of p-doping (SP- versus defect-induced) which turns out to be essentially additive.